Arithmetic or arithmetics (from the Greek word αριθμός = number) in common usage is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numerals, though in usage by professional mathematicians, it often is treated as synonym for number theory.

The traditional arithmetic operations are addition, subtraction, multiplication and division, although more advanced operations (such as manipulations of percentages, square root, exponentiation, and logarithmic functions) are also sometimes included in this subject.

The arithmetic of natural numbers, integers, rational numbers (in the form of vulgar fractions), and real numbers (using the decimal place-value system known as algorism) is typically studied by schoolchildren, who learn manual algorithms for arithmetic.

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Arithmetic is a branch of mathematics which records elementary properties of certain arithmetical operations on numbers.

The arithmetic of natural numbers, integers, rational numbers (in the form of fractions) and real numbers (in the form of decimal expansions[?]) is typically studied by schoolchildren of the elementary grades.

The term"arithmetic" is also sometimes used to refer to number theory; it's in this context that one runs across the fundamentaltheorem of arithmetic and arithmetical functions.

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The fundamentaltheorem of arithmetic is the statement that every positive integer can be written as a product of prime numbers in a unique way.

To make the theorem work even for the number 1, we think of 1 as being the product of zero prime numbers.

Essentially, the theorem establishes the importance of prime numbers: they are the "basic building blocks" of the positive integers in that every positive integer can be put together from primes in a unique fashion.

Arithmetic or arithmetics is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numerals.

The arithmetic of natural numbers, integers, rational numbers (in the form of fractions), and real numbers (using the decimal place-value system known as algorism) is typically studied by schoolchildren, who learn manual algorithms for arithmetic.

It is easy to factor a small number like six, but one of the fundamental truths of math, named the fundamentaltheorem of arithmetic, is that all integers can be expressed as the product of their prime factors.

The fundamentaltheorem of arithmetic implies that prime numbers are important cornerstones in number theory because they are the building blocks from which all other numbers are constructed.

Because the fundamentaltheorem of arithmetic establishes prime numbers as the building blocks of composite numbers, many mathematicians of note have attempted to describe a quick and decisive algorithm that will determine whether a given number is prime or composite.

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PlanetMath: proof of the fundamentaltheorem of arithmetic

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The fundamentaltheorem of arithmetic states that any composite number can be written as the product of prime numbers, called its prime factors, in one and only one way (provided that the order of the factors is not taken into account).

Fermat considered Pythagoras' theorem, which states that, for every right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

His proof of Fermat's last theorem is likely to be remembered as one of the greatest ever mathematical achievements.

We can reword the FundamentalTheorem this way: the canonical factorization of an integer greater than one is unique.

This theorem (and indeed any theorem labeled "fundamental") should not be taken too lightly.

Basically two properties: first, that every integer can be written as a product of primes (this is a simple consequence of the well ordering principle); and second, if a prime p divides ab, then p divides a or b (this is sometimes used as the definition of prime, see the entry prime number).